Updated at 1:27 p.m ET: SANFORD, Fla. -- Civil-rights leaders from the NAACP and other groups led thousands of other protesters on Saturday in a march to the city’s police headquarters to demand the arrest of the man who shot and killed Trayvon Martin.

The Rev. Jesse Jackson, the Rev. Al Sharpton and NAACP President Benjamin Jealous were among those leading the rally through Sanford’s streets, marching behind a huge yellow banner with the words “Justice for Trayvon.”

With gospel music playing in the background, protesters were marching from a technical high school campus on 13th Street through a predominantly black neighborhood to the Sanford Police Station several blocks away. The throng stretched for blocks, weaving past homes, churches and small businesses, many of them boarded up.

The rally was organized by the NAACP. Its chapters from South Carolina, Georgia and Alabama arranged buses to bring participants to the rally, while others traveled by car.

"Because of the age of the young man and because of the circumstances of his death, every community can identify with that," said Bernard Simelton, president of the Alabama state conference of the NAACP. "We've had things like that happen in Alabama where somebody gets killed and the police just sweep it under the rug. It just touches everyone."

The marchers were demanding the arrest of George Zimmerman, the 28-year-old neighborhood watchman who says he was defending himself when he fatally shot 17-year-old Martin during a scuffle. Martin, who was black, was unarmed as he walked from a convenience store, and the case has become a racial flashpoint with protesters across the nation calling for his arrest. Zimmerman's father is white, his mother Hispanic.

NAACP President and CEO Ben Jealous joins MSNBC to discuss the investigation into the death of Trayvon Martin.

Sanford police did not immediately arrest Zimmerman, saying they had no information to disprove his assertion that he acted in self-defense. A special prosecutor has since been named to look into the case.

At a press conference before the march, Jealous and Sharpton denied media reports that Sharpton planned to call for an economic boycott of Sanford or the surrounding central Florida area, calling it a "media fabrication."

"Put to rest the rumor that there is any discussion of a boycott of the community," Jealous told reporters.

Sharpton said there could still be unspecified action against national corporations that support the "Stand Your Ground" laws like the one police cited when they declined to arrest Zimmerman. The law gives citizens wide latitude to use deadly force when a threat is perceived.

Sharpton declined to identify those corporations but said, "We take nothing nonviolent off the table."

A Florida NAACP leader said that Sanford Police Chief Bill Lee’s stepping aside temporarily was not enough, and that he should be fired.

Martin’s death has also attracted international attention.

About 300 people gathered outside the U.S. Embassy in London on Saturday in a show of solidarity for the Martin family's cause. Some read poems and others carried placards with the slogan 'No Justice, No peace.' At the end of the three-hour vigil, 17 black balloons where released in honor of the slain teenager.